Fedosov, B. V. Deformation quantization and asymptotic operator representation. (English. Russian original) Zbl 0737.47042 Funct. Anal. Appl. 25, No. 3, 184-194 (1991); translation from Funkts. Anal. Prilozh. 25, No. 3, 24-36 (1991). The asymptotic operator representation (AOR) based on the theory of pseudodifferential operators is studied in connection with the deformation quantization. The special local (AOR) defines the Čech 2- cocycle on certain variety. It is shown that if this cocycle gives a certain cohomology class, then the local (AOR) can be extended to the global one. Reviewer: J.Kolomý (Praha) Cited in 3 ReviewsCited in 5 Documents MSC: 47G30 Pseudodifferential operators 47B99 Special classes of linear operators Keywords:asymptotic operator representation; pseudodiffeential operators; deformation quantization; Chech 2-cocycle × Cite Format Result Cite Review PDF Full Text: DOI References: [1] M. V. Karasev and V. P. Maslov, ”Asymptotic and geometric quantization,” UMN,39, No. 6, 145-173 (1984). [2] A. Lichnerowicz, Global Theory of Connections and Holonomy Groups [Russian translation], IL, Moscow (1960). [3] B. V. Fedosov, ”Quantization and index,” Dokl. Akad. Nauk SSSR,291, No. 1, 82-86 (1986). · Zbl 0635.58019 [4] B. V. Fedosov, ”An index theorem in the algebra of quantum observables,” Dokl. Akad. Nauk SSSR,305, No. 4, 835-838 (1989). [5] B. V. Fedosov, Index Theorems [in Russian] (in press). · Zbl 0884.58087 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.